WordPress archive posts returns user to homepage

are you using archives widget?
if not then which function you are calling to get archives.

try to add this code (below) in your sidebar.

<?php $archives = wp_get_archives('type=monthly&limit=10&echo=0');
if ($archives) { ?>
  <ul class="archive-list">
     <?php echo $archives; ?>
  </ul>
<?php } ?>

this will output as an unordered list of last 10 monthly archives, you can change limit and type to weekly or as needed.

for more information about wp_get_archives found on codex here